Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the di...Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the discounted dividend payments until ruin is derived. Moreover, under a very relaxed condition, the solutions for arbitrary moments are obtained by setting up iteration processes because of a special property of the system of integral equations.展开更多
In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend pa...In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived. Third, by a ＂differential＂ argument, the time to recovery to zero from a given negative surplus is considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed.展开更多
In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new stra...In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy （even that of the optimal dividend strategy）. Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang （2） and compound Poisson risk models are also given.展开更多
基金supported by the Natural Sciences Foundation of China under Grant No.10871064
文摘Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the discounted dividend payments until ruin is derived. Moreover, under a very relaxed condition, the solutions for arbitrary moments are obtained by setting up iteration processes because of a special property of the system of integral equations.
基金Supported by the National Natural Science Foundation of China (10971157)the Fundamental Research Funds for the Central Universities
文摘In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived. Third, by a ＂differential＂ argument, the time to recovery to zero from a given negative surplus is considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed.
基金Supported by National Natural Science Foundation of China(Grant No.10871064)Scientific Research Funds of Hu'nan Provincial Education Department(08C883)Hu'nan Provincial Science and Technology Department(2009FJ3141)
文摘In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy （even that of the optimal dividend strategy）. Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang （2） and compound Poisson risk models are also given.
